nine odd numbers have a sum of 243.find the sum of the first and last numbers in a set of numbers. hint:if three numbers when added equals twelve then represent it by adding n+()n+1.
To find the sum of the first and last numbers in a set of numbers, we need to determine the value of the first and last numbers.
We are given that the sum of nine odd numbers is 243. Since odd numbers have the form 2n+1, where n is an integer, we can represent the sum of these nine odd numbers as follows:
(2n+1) + (2n+1) + (2n+1) + (2n+1) + (2n+1) + (2n+1) + (2n+1) + (2n+1) + (2n+1) = 243
Simplifying the equation, we get:
9(2n+1) = 243
Divide both sides by 9 to isolate (2n+1):
2n+1 = 243/9
2n+1 = 27
Now, subtract 1 from both sides to solve for n:
2n = 27 - 1
2n = 26
Divide both sides by 2 to solve for n:
n = 26/2
n = 13
So, the first odd number in the set is 2n+1 = 2(13)+1 = 27.
To find the last odd number, we can simply add 2 to the first odd number:
27 + 2 = 29
Now, we can calculate the sum of the first and last numbers:
Sum = 27 + 29 = 56
Therefore, the sum of the first and last numbers in the set is 56.